A) \[\frac{2}{\sqrt{3}}\]
B) \[\sqrt{3}\]
C) \[2\]
D) None of these
Correct Answer: A
Solution :
\[\int_{1}^{x}{\frac{dt}{\left| \,t\, \right|\,\sqrt{{{t}^{2}}-1}}}=\frac{\pi }{6}\] \[\Rightarrow \] \[[{{\sec }^{-1}}t]_{1}^{x}=\frac{\pi }{6}\] \[\Rightarrow \] \[{{\sec }^{-1}}x-{{\sec }^{-1}}1=\frac{\pi }{6}\] \[\Rightarrow \] \[{{\sec }^{-1}}x-0=\frac{\pi }{6}\] \[\Rightarrow \] \[x=\sec \frac{\pi }{6}\] \[\Rightarrow \] \[x=\frac{2}{\sqrt{3}}\]
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